In recent years, Dynamic MRI has gained popularity and acceptance in clinical settings due to its ability to reveal spatial and temporal information in cardiovascular and neuroimaging studies. One of the challenges of dynamic MRI is that it requires a relatively long acquisition time compared to other medical imaging modalities such as X-ray CT. In order to fit the data acquisition time inside the motion cycles of the imaging subject, the acquired data is typically undersampled.
The undersampling inherent in dynamic MRI may be addressed through the use of Compressed Sensing (CS) techniques. Using CS, a signal may be represented using a few nonzero coefficients of a dictionary or a sparse transform. Both the dictionary and the transform can be either an orthonormal system or an over-complete system. However, the latter is generally preferable because it possesses the advantage of sparsifying the signal under a redundant system. Fixed tight frame systems, such as ridgelet, curvelet, bandlet, and shearlet, are over-complete systems that may be suitable for a dictionary or sparse transform. However, a fixed tight frame may not be optimal in applications where there is variety among the subject being imaged. For example, in medical applications, a fixed tight frame may produce poor results because the texture in a medical image varies based on, for example, the tissue type being imaged or the acquisition protocol.